Question: Simplify the following expression: $ t = \dfrac{6}{-3z - 9} + \dfrac{-7}{4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{6}{-3z - 9} \times \dfrac{4}{4} = \dfrac{24}{-12z - 36} $ Multiply the second expression by $\dfrac{-3z - 9}{-3z - 9}$ $ \dfrac{-7}{4} \times \dfrac{-3z - 9}{-3z - 9} = \dfrac{21z + 63}{-12z - 36} $ Therefore $ t = \dfrac{24}{-12z - 36} + \dfrac{21z + 63}{-12z - 36} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{24 + 21z + 63}{-12z - 36} $ $t = \dfrac{21z + 87}{-12z - 36}$ Simplify the expression by dividing the numerator and denominator by -3: $t = \dfrac{-7z - 29}{4z + 12}$